Vaishnavy V et. al. / International Journal of Modern Sciences and Engineering Technology (IJMSET)
ISSN 2349-3755; Available at https://www.ijmset.com
Volume 2, Issue 3, 2015, pp.93-101
© IJMSET-Advanced Scientific Research Forum (ASRF), All Rights Reserved
“IJMSET promotes research nature, Research nature enriches the world’s future”
93
ON INTUITIONISTIC FUZZY ALMOST REGULAR GENERALIZED
SEMIPRE CONTINUOUS MAPPINGS
Abstract
In this paper, we introduce the notion of intuitionistic fuzzy almost regular generalized semipre
continuous mappings. Furthermore we provide some properties of intuitionistic fuzzy almost regular
generalized semipre continuous mappings and discuss some fascinating theorems.
Keywords: Intuitionistic fuzzy sets, Intuitionistic fuzzy topology, Intuitionistic fuzzy regular generalized semipre
closed sets, Intuitionistic fuzzy regular generalized semipre open sets, Intuitionistic fuzzy almost regular generalized semipre
continuous mappings.
1 INTRODUCTION:
The notion of intuitionistic fuzzy sets by Atanassov [1] was a breakthrough towards the
evolution of intuitionistic fuzzy topology. Using this notion, Coker [3] constructed the basic concepts
of intuitionistic fuzzy topological spaces. Later this was followed by the introduction of intuitionistic
fuzzy regular generalized semipreclosed sets by Vaishnavy, V and Jayanthi, D [11] in 2015 which
was simultaneously followed by the introduction of intuitionistic fuzzy regular generalized semipre
continuous mappings [13] by the same authors. We now extend our idea towards intuitionistic fuzzy
almost regular generalized semipre continuous mappings and discuss some of their properties.
2 PRELIMINARIES
Definition 2.1 [1]: An intuitionistic fuzzy set (IFS in short) A is an object having the form
A={ۦx, ȝ
A
(x), Ȟ
A
(x) : x ∈ X}
where the function ȝ
A
: X ⟶ [0,1] and Ȟ
A
: X ⟶ [0,1] denote the degree of membership
(namely ȝ
A
(x)) and the degree of non membership (namely Ȟ
A
(x)) of each element x ∈ X to the set A,
respectively, and 0 ≤ ȝ
A
(x) + Ȟ
A
(x) ≤ 1 for each x ∈ X. Denote by IFS(X), the set of all intuitionistic
fuzzy sets in X.
An intuitionistic fuzzy set A in X is simply denoted by A=ۦx, ȝ
A
, Ȟ
A
instead of denoting
A={ۦx, ȝ
A
(x), Ȟ
A
(x) : x ∈ X}.
Definition 2.2 [1] : Let A and B be two IFSs of the form
A={ۦx, ȝ
A
(x), Ȟ
A
(x) : x ∈ X}
and
B={ۦx, ȝ
B
(x), Ȟ
B
(x) : x ∈ X}.
Then,
(a) A كB if and only if ȝ
A
(x) ≤ ȝ
B
(x) and Ȟ
A
(x) ≥ Ȟ
B
(x) for all x ∈ X
Vaishnavy V
1
M.Sc Mathematics,
Avinashilingam University, Coimbatore,
Tamil Nadu, India
vaishnavyviswanathan92@gmail.com
Jayanthi D
2
Assistant Professor of Mathematics,
Avinashilingam University, Coimbatore,
Tamil Nadu, India
jayanthimaths@rediffmail.com